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Том 16   Выпуск 1   Год 2021
Хасан Агдауи1, Мухсин Тилиуа1, Коттаккаран Суппи Нисар2, Ильяс Хан3

Эпидемическая модель дробного порядка с ядром Миттаг-Леффлера для эпидемии COVID-19

Математическая биология и биоинформатика. 2021;16(1):39-56.

doi: 10.17537/2021.16.39.

Список литературы

  1. Atangana A. Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination? Chaos, Solitons & Fractals. 2020;136:109860. doi: 10.1016/j.chaos.2020.109860
  2. Atangana A., Araz S.I. Mathematical model of COVID-19 spread in Turkey and South Africa: Theory, methods and applications. Advances in Difference Equations. 2020;2020(1):1-89. doi: 10.1101/2020.05.08.20095588
  3. Yang Y., Lu Q., Liu M., Wang Y., Zhang A., Jalali N., Dean N.E., Longini I., Halloran M.E., Xu B., et al. Epidemiological and clinical features of the 2019 novel coronavirus outbreak in China. medRxiv. 2020;2020(1):1-89. doi: 10.1101/2020.02.10.20021675
  4. Diekmann O., Heesterbeek J.A.P., Metz J.A.J. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology. 1990;28(4):365-382. doi: 10.1007/BF00178324
  5. World Health Organization Website. https://www.who.int/ (accessed 29.04.2021).
  6. Atangana A., Alkahtani B.S. Analysis of the Keller–Segel model with a fractional derivative without singular kernel. Entropy. 2015;17(6):4439-4453. doi: 10.3390/e17064439
  7. Atangana A., Baleanu D. New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model. Thermal Science. 2016;20:763-769. doi: 10.2298/TSCI160111018A
  8. Atangana A., Koca I. On the new fractional derivative and application to nonlinear Baggs and Freedman model. J. Nonlinear Sci. Appl. 2016;9(5):2467-2480. doi: 10.22436/jnsa.009.05.46
  9. Yavuz M., Özdemir N., Baskonus H.M. Solutions of partial differential equations using the fractional operator involving Mittag-Leffler kernel. The European Physical Journal Plus. 2018;133(6):1-11. doi: 10.1140/epjp/i2018-12051-9
  10. Saad K.M., Deniz S., Baleanu D. On a new modified fractional analysis of Nagumo equation. International Journal of Biomathematics. 2019;12(03):1950034. doi: 10.1142/S1793524519500347
  11. Yusuf A., Qureshi S., Inc M., Aliyu A.I., Baleanu B., Shaikh A.A. Two-strain epidemic model involving fractional derivative with Mittag-Leffler kernel. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2018;28(12):123121. doi: 10.1063/1.5074084
  12. Bildik N., Deniz S. A new fractional analysis on the polluted lakes system. Chaos, Solitons & Fractals. 2019;122:17-24. doi: 10.1016/j.chaos.2019.02.001
  13. Uçar S. Existence and uniqueness results for a smoking model with determination and education in the frame of non-singular derivatives. Discrete Contin. Dyn. Syst. Ser. A. 2018:1-17. doi: 10.3934/dcdss.2020178
  14. Hethcote H. The mathematics of infectious diseases. SIAM Review. 2000;42(4):599-653. doi: 10.1137/S0036144500371907
  15. Brauer F. Mathematical epidemiology: Past, present, and future. Infectious Disease Modelling. 2017;2(2):113-127. doi: 10.1016/j.idm.2017.02.001
  16. Yang C., Wang J. A mathematical model for the novel coronavirus epidemic in Wuhan, China. Mathematical Biosciences and Engineering. 2020;17(3):2708. doi: 10.3934/mbe.2020148
  17. Khan M.A., Ullah S., Farooq M. A new fractional model for tuberculosis with relapse via Atangana–Baleanu derivative. Chaos, Solitons & Fractals. 2018;116:227-238. doi: 10.1016/j.chaos.2018.09.039
  18. Khan M.A., Atangana A. Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative. Alexandria Engineering Journal. 2020;59(4):2379-2389. doi: 10.1016/j.aej.2020.02.033
  19. Ullah M.Z., Alzahrani A.K., Baleanu D. An efficient numerical technique for a new fractional tuberculosis model with nonsingular derivative operator. Journal of Taibah University for Science. 2019;13(1):1147-1157. doi: 10.1080/16583655.2019.1688543
  20. Khan M.A., Atangana A. Dynamics of Ebola Disease in the Framework of Different Fractional Derivatives. Entropy. 2019;21(3):303. doi: 10.3390/e21030303
  21. Khan M.A., Ismail M., Ullah S., Farhan M. Fractional order SIR model with generalized incidence rate. AIMS Mathematics. 2020;5(3):1856-1880. doi: 10.3934/math.2020124
  22. The Moroccan Ministry of Public Health, COVID-19 Platform. http://www.covidmaroc.ma/Pages/AccueilAR.aspx (accessed 29.04.2021).
  23. Shaikh A.S., Shaikh I.N., Nisar K.S. A Mathematical Model of COVID-19 Using Fractional Derivative: Outbreak in India with Dynamics of Transmission and Control. Advances in Difference Equations. 2020;2020(1):1-19. doi: 10.20944/preprints202004.0140.v1
  24. Shaikh A.S., Jadhav V.S., Timol M.G., Nisar K.S., Khan I. Analysis of the COVID-19 Pandemic Spreading in India by an Epidemiological Model and Fractional Differential Operator. Preprints. 2020:1-16. doi: 10.20944/preprints202005.0266.v1
  25. Kermack W.O., McKendrick A.G. A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical haracter. 1927;115(772):700-721. doi: 10.1098/rspa.1927.0118
  26. Prakasha D.G., Veeresha P., Baskonus H.M. Analysis of the dynamics of hepatitis E virus using the Atangana-Baleanu fractional derivative. The European Physical Journal Plus. 2019;134(5):1-11. doi: 10.1140/epjp/i2019-12590-5
  27. Mekkaoui T., Atangana A. New numerical approximation of fractional derivative with non-local and non-singular kernel: application to chaotic models. The European Physical Journal Plus. 2017;132(10):1-16. doi: 10.1140/epjp/i2017-11717-0
  28. Atangana A., Owolabi K.M. New numerical approach for fractional differential equations. Mathematical Modelling of Natural Phenomena. 2018;13(1):3. doi: 10.1051/mmnp/2018010
  29. Rihan F.A., Al-Mdallal Q.M., AlSakaji H.J., Hashish A. A fractional-order epidemic model with time-delay and nonlinear incidence rate. Chaos, Solitons & Fractals. 2019;126:97-105. doi: 10.1016/j.chaos.2019.05.039
  30. Ahmad S., Ullah A., Al-Mdallal Q.M., Khan H., Shah K., Khan A. Fractional order mathematical modeling of COVID-19 transmission. Chaos, Solitons & Fractals. 2020;139:110256. doi: 10.1016/j.chaos.2020.110256
  31. Asif M., Khan Z.A., Haider N., Al-Mdallal Q. Numerical simulation for solution of SEIR models by meshless and finite difference methods. Chaos, Solitons & Fractals. 2020;141:110340. doi: 10.1016/j.chaos.2020.110340
  32. Asif M., Jan S.U., Haider N., Al-Mdallal Q., Abdeljawad T. Numerical modeling of NPZ and SIR models with and without diffusion. Results in Physics. 2020;19:103512. doi: 10.1016/j.rinp.2020.103512
  33. Hajji M.A., Al-Mdallal Q. Numerical simulations of a delay model for immune system-tumor interaction. Sultan Qaboos University Journal for Science. 2018;23(1):19-31. doi: 10.24200/squjs.vol23iss1pp19-31
  34. Thabet S.T.M., Abdo M.S., Shah K., Abdeljawad T. Study of transmission dynamics of COVID-19 mathematical model under ABC fractional order derivative. Results in Physics. 2020;19:103507. doi: 10.1016/j.rinp.2020.103507

 
Содержание
Оригинальная статья
Мат. биол. и биоинф.
2021;16(1):39-56
doi: 10.17537/2021.16.39
опубликована на англ. яз.

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